During my sixth year of teaching, I asked the class to divide a five-digit number by a two-digit number. For middle schoolers, this felt like a straightforward task. I walked around the classroom to see how everyone was approaching their work. Suddenly, I stopped at one of the students’ desks and said, “Are you playing Hang Man in my class?”. Of course he wasn’t, but I needed a way into his work. He explained how he learned to divide using a method they’re calling “repeated subtraction.” Rather than getting the exact number of times the divisor goes into the dividend, this method gives him multiple opportunities to find the number of divisor groupings that could fit into the dividend. But at first, I was confused why that worked. Actually, I think my face rebuked it.
I asked, “How did you do that?” and watched the student do it and explain it to me. Oh, and then I went home and tried it, too.
Before I found the quotient, I kept thinking about all this newer math my students did before they got to middle school. The lattice method of multiplication. Making tens. Area models. The growing list of pedagogical methods and approaches that differed from how my generation and previous generations learned math continues to press on. More of my people from different walks of life are asking me “What’s up with this new math?” But after I explain it to them, I still don’t feel satisfied with my answer.
Ultimately, it boils down to whether schools can do a good job of telling families why we’re doing what we’re doing. And we’re not. Let me explain.
Body of Knowledge Things
For the most part, teachers believe themselves to have a body of knowledge that they should be trusted with. As a former teacher, I took a lot of pride in my credentials. I not only had a computer science degree in undergrad with lots of math, but also a masters’ program that prepared me well. My day-to-day preparation consisted of thinking about how students individually and collectively would get my material. That’s not easy. The mental math teachers do to teach a topic well over a handful of days is worth honoring.
But there’s a difference between “is trusted” and “should be trusted.” Right now, teachers don’t feel trusted, even those with multiple credentials.
The lack of trust isn’t just at the interpersonal level. Teachers consistently encounter peers, leadership, and families who don’t fully trust teachers to do their work well. This sometimes forces teachers to double down on ideas of respect, even closing them off to other ideas and into their work. But also, because society has generally deprofessionalized work across the board, society also proliferates the idea that teachers don’t have a real body of knowledge.
In education, much of this sentiment comes from people who don’t have children in their care.
This feels even more poignant in math class where some – not all – teachers still feel a way about having anyone who’s not an educator critiquing their work. For generations, we’ve had ideas about foundational math that have been passed down time and again with little disruption. We know what the algorithms for long division, addition/multiplication of two+ digit numbers, and operations with fractions look like. Despite the overabundance of PD providers out there, many teachers generally stick with teaching math how they were taught. That’s not a bad thing, but it’s worth keeping in mind because …
Teachers and Families May Have Gone To Similar Schools of Thought
If we’re all familiar with the aforementioned algorithms, it stands to reason that we were almost all taught similarly. That’s wild to think about. When Sputnik and the 1957 National Defense Education Act ushered new attention on STEM, a “New Math” found its era. Yet, the “New Math” is the same math that generations of us remember. Fast forward to now and many of the memes we’ve seen about Common Core math only underscore the disconnect between all these generations and the current one.
So, if traditional methods stuck for teachers, imagine how people who aren’t getting PD about this stuff believe.
Sometimes, our collective memory does us a disservice. We might believe that, because the mathematical content we learned worked for us individually, it means that the rest of us also got it the same way. We may have seen our peers graduate with us, an indication that an authority believed we were equally competent at the same work. Some of us even went to college. Having a seat in college presumes that everyone at the college passed elementary school math, if not secondary math.
Many of the methods we believed to be effective for us needed a course correction. When people used algorithms to add three digit numbers by other three digit numbers, they may have “carried the one” without understanding that the one may have represented a 10 or 100. When people tried long division, they may have quit somewhere in between because the divisor’s multiples were too complicated.
More broadly, the math we thought we knew might have failed for all the maths we left behind. Our collective memory may fail us, too.
The New Math as a Reclamation
I’ve had people across different identity groups proclaiming that we should get back to basics. I empathize, but I always point us to the idea of the toolbox. For too long, the average person only had a handful of tools to solve math problems. We kept using a hammer every time we saw problems that required a hammer and ones that required a screwdriver or a wrench. As we get older, however, we notice that good mathematicians have a plethora of tools in their toolbox, many of which they don’t have to use, but they’re comfortable with.
The same people who say “But American students can’t compete internationally with math scores” also like their schools unequal, especially when it comes to math.
One way to build the bridge from the traditional math to the new math is to communicate why these new maths help. It’s not the solution, but families deserve to know why teachers do what they do with math. Often, during parent-teacher conferences, I sat there and taught parents a little math so they can take the math home. Other schools have found ways to give parents and families math workshops so they have access to this stuff as well.
Thinking back to my previous example, the repeated subtraction method of division is a more elegant way of doing long division. It requires similar attention to multiples and remainders, but less stress on getting the exact number of groupings towards a quotient. That doesn’t require an expert from on high to say as much.
Sometimes, we just need to do it ourselves, then show others. In community hopefully.
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